Question

Let X and Y be two independent exponential random variables. Denote X as the time until...

Let X and Y be two independent exponential random variables. Denote X as the time until Bob comes with average waiting time 1/lamda (lambda > 0). Denote Y as the time until Gary comes with average waiting time 1/mu (mu >0). Let S be the time before both of them come.
a) What is the distribution of S?
b) Derive the probability mass function of T defined by T=0 if Bob comes first and T=1 if Gary comes first.
c) Are S and T independent?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X and Y be independent exponential random variables with respective rates ? and ? Is...
Let X and Y be independent exponential random variables with respective rates ? and ? Is max(X, Y ) an exponential random variable?
fXYx,y=ke-3x+23 y The joint distribution of two random variables are given above. Let X denote the...
fXYx,y=ke-3x+23 y The joint distribution of two random variables are given above. Let X denote the interarrival time for packages at a network device and let Y denote the service time of a package in the device. [10pts] what is the expected interarrival time to this network element. (hint calculate k first) [5pts] What is the covariance of X and Y [10pts] If a random variable Z is to be defined as Z=X+Y, What is the expected value of Z
X, T are independent exponential random variables with parameters Lambda(X) and Lambda(T). Find the conditional density...
X, T are independent exponential random variables with parameters Lambda(X) and Lambda(T). Find the conditional density of X given X<T
Let X and Y be independent exponential random variables with respective parameters 2 and 3. a)....
Let X and Y be independent exponential random variables with respective parameters 2 and 3. a). Find the cdf and density of Z = X/Y . b). Compute P(X < Y ). c). Find the cdf and density of W = min{X,Y }.
STAT 180 Let X and Y be independent exponential random variables with mean equals to 4....
STAT 180 Let X and Y be independent exponential random variables with mean equals to 4. 1) What is the covariance between XY and X. 2) Let Z = max ( X, Y). Find the Probability Density Function (PDF) of Z. 3) Use the answer in part 2 to compute the E(Z).
Problem 0.1 Suppose X and Y are two independent exponential random variables with respective densities given...
Problem 0.1 Suppose X and Y are two independent exponential random variables with respective densities given by(λ,θ>0) f(x) =λe^(−xλ) for x>0 and g(y) =θe^(−yθ) for y>0. (a) Show that Pr(X<Y) =∫f(x){1−G(x)}dx {x=0, infinity] where G(x) is the cdf of Y, evaluated at x [that is,G(x) =P(Y≤x)]. (b) Using the result from part (a), show that P(X<Y) =λ/(θ+λ). (c) You install two light bulbs at the same time, a 60 watt bulb and a 100 watt bulb. The lifetime of the...
Let X1,...,X99 be independent random variables, each one distributed uniformly on [0, 1]. Let Y denote...
Let X1,...,X99 be independent random variables, each one distributed uniformly on [0, 1]. Let Y denote the 50th largest among the 99 numbers. Find the probability density function of Y.
Assume that X and Y are independent random variables, each having an exponential density with parameter...
Assume that X and Y are independent random variables, each having an exponential density with parameter λ. Let Z = |X - Y|. What is the density of Z?
Let X and Y be independent and normally distributed random variables with waiting values E (X)...
Let X and Y be independent and normally distributed random variables with waiting values E (X) = 3, E (Y) = 4 and variances V (X) = 2 and V (Y) = 3. a) Determine the expected value and variance for 2X-Y Waiting value µ = Variance σ2 = σ 2 = b) Determine the expected value and variance for ln (1 + X 2) c) Determine the expected value and variance for X / Y
Assume two random variables X and Y satisfy the following joint PDF, fXY (x, y) =...
Assume two random variables X and Y satisfy the following joint PDF, fXY (x, y) = { 2, x + y ≤ 1 x, y ≥ 0, 0, otherwise.} (a) Find the values of E[X + Y ] and E[X − Y ]. (b) Derive g(s) = E[X − Y |X + Y = s] for any given s. (c) Derive h(t) = E[X + Y |X − Y = t] for any given t.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT